Failure-mode Transition Speed in Three- Dimensional Transient Deformations of a Microporous Heat-conducting Thermoelastoviscoplastic Prenotched Plate

We analyze three-dimensional finite coupled thermomechanical deformations of a rectangular plate with two parallel notches placed symmetrically about the horizontal centroidal plane of the plate. The edge surface of the plate between the two notches is struck by a cylindrical projectile of diameter equal to the distance between the notches and made of the same material as the plate. The plate material is modeled as heat-conducting, microporous, elastoviscoplastic, and isotropic. Both the brittle and the ductile failures initiate at points adjoining the notch-tip surface that are on the midplane of the plate and propagate toward the outer surfaces. Even for a relatively thin plate, the difference in the times of initiation of failures on the mid and front surfaces is significant. Also the two failure modes on the mid surface initiate much later than that predicted by the plane strain analysis. Thus an experimentalist observing fracture on the front or the back face of the plate will see it initiate much later than the times given by the plane strain analysis of the problem. For a steel plate, it is found that the failure mode transitions from brittle to ductile at an impact speed of about 21.8m=s.